A note on the geometry of Bayesian global and local robustness

✍ Scribed by M.Perone Pacifico; G. Salinetti; L. Tardella

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 687 KB
• Volume: 69
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(97)00125-0

✦ Synopsis

In this paper a geometric interpretation of the main quantities of interest in Bayesian robustness is presented. It helps in visualizing the relationships among global robustness, local sensitivity measures based on functional derivatives and the so-called linearization technique. An immediate geometric representation of general tools, already available in the literature on finite-dimensional fractional optimization, suggests an efficient algorithm to get the range of ratio linear functionals. The geometric understanding is also used to obtain the range of a local sensitivity measure and hence the probability measures in a class that are locally most (least) robust. Some inequalities are derived connecting the global range of the quantity of interest with local sensitivity measures based on the Gateaux derivative, leading to further considerations about the calibration of the local sensitivity. (~